Stability of superheavy nuclei

The potential-energy surfaces of an extended set of heavy and superheavy even-even nuclei with $92\le Z\le 126$ and isospins $40\le N-Z\le 74$ are evaluated within the recently developed Fourier shape parametrization. Ground-state and decay properties are studied for 324 different even-even isotopes in a four-dimensional deformation space, defined by nonaxiality, quadrupole, octupole, and hexadecapole degrees of freedom. Nuclear deformation energies are evaluated in the framework of the macroscopic-microscopic approach, with the Lublin-Strasbourg drop model and a Yukawa-folded mean-field potential. The evolution of the ground-state equilibrium shape (and possible isomeric, metastable states) is studied as a function of $Z$ and $N$. $\alpha$-decay $Q$ values and half-lives, as well as fission-barrier heights, are deduced. In order to understand the transition from asymmetric to symmetric fission along the Fm isotopic chain, the properties of all identified fission paths are investigated. Good agreement is found with experimental data wherever available. New interesting features about the population of different fission modes for nuclei beyond Fm are predicted.

Figure 1

Schematic visualization, in cylindrical coordinates, of the parameters entering the definition of the profile function defined by Eq. (4). The quantities $z_{\mathrm{l}}$ and $z_{\mathrm{r}}$ localize the mass centers of left and right nascent fragments entering the definition of $R_{12}=z_{\mathrm{r}}-z_{\mathrm{l}}$.

Figure 2

Visualization of the relation between the ($\beta ,\gamma$) and the ($q_2^{},\eta$) deformation coordinates.

Figure 3

Deformation energy of ${}^{280}\mathrm{Ds}$ on the $(q_2,q_3)$ plane for $\eta =0$ minimized with respect to $q_4$ (top left) and on the $(q_2,\eta )$ plane minimized with respect to $q_3$ and $q_4$ (top right). The $(q_4,q_3)$ and $(q_4,\eta )$ cross sections around the oblate and prolate minima are shown in the middle and bottom rows, respectively.

Figure 4

Same as in Fig. 3 but for ${}^{276}\mathrm{Cn}$.

Figure 5

Values of the collective coordinates (${\eta }^{\mathrm{eq}},q_2^{\mathrm{eq}},q_3^{\mathrm{eq}},q_4^{\mathrm{eq}}$) (from top to bottom) at equilibrium deformation defined as the ground-state minimal-energy configuration on the ($N-Z,Z$) plane. The circles denote already discovered isotopes and the thick (pink) line shows the $\beta$-stable nuclei. The thin (black) lines correspond to the constant mass number $A$.

Figure 6

Ground-state microscopic contribution to the potential energy for the nuclei of Fig. 5.

Figure 7

Ground-state microscopic contribution to the potential energy along isotopic chains between U and Hs (top), between Ds and Og (middle), and between elements $Z=120$ and $Z=126$ (bottom).

Figure 8

Deformation energy in the ($q_2,\eta$) (upper half) and ($q_2,q_3$) (lower half) subspaces for three isotopes of Hs (first row), Sg (second row), and Rf (third row). Each column corresponds to a specific $N-Z$ value: 52 (left), 54 (middle), and 56 (right).

Figure 9

Calculated $Q_{\alpha }$ energies for different isotopic chains compared to the experimental data (red crosses) [36] where available.

Figure 10

Calculated $T_{1/2}^{\alpha }$ $\alpha$-decay half-lives on a logarithmic scale for different isotopic chains compared to the experimental data (red crosses) [37] where available. Two theoretical estimates given by the open black and full blue circles are shown (see the text).

Figure 11

Fission barrier height for the considered nuclei as a function of $Z$ and $N-Z$.

Figure 12

Similar to Figs. 9 and 10 for calculated fission-barrier heights compared to the experimental estimates [45, 46, 47, 48].

Figure 13

Deformation energy in the ($q_2,q_3$) plane minimized with respect to $\eta$ and $q_4$, for ${}^{252}\mathrm{Cf}$ and ${}^{254–258}\mathrm{Fm}$.

Figure 14

Deformation energy in the ($q_4,q_3$) plane for $q_2=1.75$, for ${}^{252}\mathrm{Cf}$ and ${}^{254–258}\mathrm{Fm}$.

Figure 15

Nuclear shape for three different sets of collective variables ($q_2,q_3,q_4$).

Figure 16

Deformation energy as in Fig. 14 at $q_2=1.75$, for ${}^{258,264}\mathrm{Rf}$ and ${}^{268,272}\mathrm{Hs}$.